• Ratenkredite
  • P. Ruppaner
  • 21.07.2020
  • Mathematik
  • Prozente und Zinsen
  • R
  • 9
  • Einzelarbeit
  • Arbeitsblatt
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1
Für den Kauf eines Lap­top nimmt Gus­tav einen Kre­dit bei einer Bank auf. Die höhe des Kre­dits be­trägt 1 500 €. Er ver­ein­bart mit der Bank fol­gen­de Be­din­gun­gen:

  • Lauf­zeit: 12 Mo­na­te
  • Mo­nat­li­cher Zins­satz: 0,42 %
  • Be­ar­bei­tungs­ge­bühr: 3 % vom Kre­dit­be­trag

a) \gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quadWie hoch ist Gus­tavs mo­nat­li­che Rate ?

Lösung1
Kre­dit­be­trag:1 500,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad1\nobreakspace500{,}00 \nobreakspace€
Be­ar­bei­tungs­ge­bühr:1 500 €  0,03 =   45,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quad1\nobreakspace500\nobreakspace€\nobreakspace\cdot\nobreakspace0{,}03\nobreakspace =\qquad\nobreakspace\nobreakspace\nobreakspace\qquad\quad45{,}00\nobreakspace€
Zin­sen:1 500 €  0,0042  12 =  75,60 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quad\qquad\qquad\quad 1\nobreakspace500\nobreakspace€\nobreakspace\cdot\nobreakspace0{,}0042\nobreakspace\cdot\nobreakspace12\nobreakspace= \qquad\nobreakspace\nobreakspace75{,}60\nobreakspace€
  \gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\nobreakspace\nobreakspace\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}
Rück­zahl­be­trag:     1 620,60 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\nobreakspace\nobreakspace\nobreakspace\nobreakspace1\nobreakspace620{,}60\nobreakspace€

Mo­nat­li­che Rate:  1 620,60 €:12=   135,05 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\nobreakspace1\nobreakspace620{,}60\nobreakspace€:12=\qquad\qquad\quad\nobreakspace\nobreakspace\nobreakspace135{,}05\nobreakspace€


Ant­wort:\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquadGus­tavs mo­nat­li­che Rate be­trägt 135,05 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 135{,}05\nobreakspace€.
b) \gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quadWie groß ist die Dif­fe­renz zwi­schen dem Kre­dit­be­trag und dem Rück­zahl­be­trag ?
Lösung
1 620,60 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quad\qquad1\nobreakspace620{,}60\nobreakspace€
​ 1 500,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad-​\nobreakspace1\nobreakspace500{,}00\nobreakspace€
   120,60 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\overline{\nobreakspace\nobreakspace\nobreakspace\quad120{,}60\nobreakspace€}


Ant­wort: Die Dif­fe­renz be­trägt 120,60 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 120{,}60\nobreakspace€
2
Gus­tav träumt von einem ei­ge­nen Auto. Das Auto kos­tet 15 000 €. Er holt sich bei zwei Au­to­häu­sern Kre­dit­an­ge­bo­te ein. Ver­glei­che die bei­den An­ge­bo­te.

Au­to­haus MEIER



Zins­satz pro Monat: 0,35 %

Be­ar­bei­tungs­ge­bühr: 1,5 %

Ab­schluss­ge­bühr (ein­ma­lig): 200 €

Lauf­zeit: 24 Mo­na­te

Au­to­haus SCHOLZ



Zins­satz pro Monat: 0,37 %

Be­ar­bei­tungs­ge­bühr: 1,9 %

Lauf­zeit: 24 Mo­na­te

\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquadBei wel­chem Au­to­haus soll Gus­tav sein Auto kau­fen ? Be­grün­de deine

\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquadEnt­schei­dung rech­ne­risch.


\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquadAu­to­haus MEIER

Lösung

Kre­dit­be­trag:  15 000,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\qquad\qquad\quad\qquad\nobreakspace\nobreakspace15\nobreakspace000{,}00 \nobreakspace€
Be­ar­bei­tungs­ge­bühr:15 000 €  0,015 =   45,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quad15\nobreakspace000\nobreakspace€\nobreakspace\cdot\nobreakspace0{,}015\nobreakspace =\qquad\nobreakspace\nobreakspace\nobreakspace\qquad45{,}00\nobreakspace€
Ab­schluss­ge­bühr: 200,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad200{,}00\nobreakspace€
Zin­sen:15 000 €  0,0035  24 =1 260,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quad\qquad\qquad\quad 15\nobreakspace000\nobreakspace€\nobreakspace\cdot\nobreakspace0{,}0035\nobreakspace\cdot\nobreakspace24\nobreakspace= \quad1\nobreakspace260{,}00\nobreakspace€
  \gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\nobreakspace\nobreakspace\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}
Rück­zahl­be­trag:   16 685,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\nobreakspace\nobreakspace16\nobreakspace685{,}00\nobreakspace€

Mo­nat­li­che Rate:  16 685 €:24   695,21 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\nobreakspace16\nobreakspace685\nobreakspace€:24\approx\qquad\qquad\qquad\nobreakspace\nobreakspace\nobreakspace695{,}21\nobreakspace€


Ant­wort:\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquadGus­tavs mo­nat­li­che Rate be­trägt 135,05 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 135{,}05\nobreakspace€.
\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquadAu­to­haus SCHOLZ
Lösung

Kre­dit­be­trag:  15 000,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\qquad\qquad\quad\qquad\nobreakspace\nobreakspace15\nobreakspace000{,}00 \nobreakspace€
Be­ar­bei­tungs­ge­bühr:15 000 €  0,019 = 285,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quad15\nobreakspace000\nobreakspace€\nobreakspace\cdot\nobreakspace0{,}019\nobreakspace =\qquad\nobreakspace\qquad285{,}00\nobreakspace€
Zin­sen:15 000 €  0,0037  24 =1332,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \quad\qquad\qquad\quad 15\nobreakspace000\nobreakspace€\nobreakspace\cdot\nobreakspace0{,}0037\nobreakspace\cdot\nobreakspace24\nobreakspace= \quad1332{,}00\nobreakspace€
  \gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\nobreakspace\nobreakspace\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}
Rück­zahl­be­trag:  16 617,00 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\nobreakspace16\nobreakspace617{,}00\nobreakspace€

Mo­nat­li­che Rate:  16 685 €:24  692,38 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\nobreakspace16\nobreakspace685\nobreakspace€:24\approx\qquad\qquad\qquad\nobreakspace\nobreakspace692{,}38\nobreakspace€




Ant­wort:\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquadDie mo­nat­li­chen Raten bei Au­to­haus SCHOLZ sind ge­rin­ger. Gus­tav soll das
  \gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \qquad\qquad\quad\nobreakspace\nobreakspaceAuto bei Au­to­haus Scholz kau­fen. Er spart ins­ge­samt 68 €\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 68\nobreakspace€.
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